Typically in Gibbs sampling (a type of MCMC method), Eq. (REF )-(REF ) are updated iteratively to dynamically evolve the Markov chain such that the network eventually reaches the Boltzmann distribution defined by Eq. (REF ). A practical difficulty lies in the serial nature of this evolution: connected nodes need to be updated one after the other since parallel updating leads to repeated oscillations in the network state, preventing the network from converging to the Boltzmann distribution. The need for sequential updating inherently serializes the network evolution, signified by the nested for-loops in standard descriptions of Gibbs sampling [1]}.
